WiMAX relay networks make resource allocation decisions once per frame. To achieve a performance gain possible under adaptive allocation. it is important to choose an appropriate practical algorithm feasible for real-time implementation. In this paper, the allocation task is considered as a two-step process and several combinations of algorithms for each step are proposed. Performance of algorithms is evaluated on a WiMAX model with variable bit rate traffic. In the authors' proposed method, they focus on multi-hop (relay based) bandwidth allocation schemes for IEEE 802.16j networks.